Consider the sequences $\left(r_{n} ight)$ and $\left(s_{n} ight)$ defined recursively by $$ r_{0}=1, \quad s_{0}=0, \quad \text { and } \quad r_{n+1)=r_{n} / 2, \quad s_{n+1)=s_{n}+r_{n+1} \quad \text { for } \quad n \geq 0 $$ CS.VS. 1119